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Polynomials

Zero Value of a Polynomial

We know that the value of a polynomial differs according to the value of the variable in it. For example, if p(x) is a polynomial with variable x and we put different values of x in p(x), then we will get different values of p(x). In some cases, the value of p(x) can be the same for two or more values of x. Also, in a few cases, the value of p(x) can be zero. 

The values of the variable at which a polynomial becomes zero are called zeroes of the polynomial. These values are very special and useful to us. Zeroes of polynomials are used in:

  • Solving problems related to [[mn:glossary]]motion[[/mn:glossary]]

  • Solving problems related to [[mn:glossary]]path[[/mn:glossary]] or [[mn:glossary]]locus[[/mn:glossary]] of a [[mn:glossary]]point[[/mn:glossary]] or geometric figure

  • Making graphs for economic [[mn:glossary]]data[[/mn:glossary]]

In this lesson, we will learn to check whether or not the given values are zeroes of the given polynomials. We will also learn to find the zeroes of different polynomials.

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Zeroes or Roots of a Polynomial 

If the value of a polynomial p(x) at x = a is zero, then a is said to be the zero or root of the polynomial p(x). Let us consider the polynomial p(x) = x2 − 5x + 6 and check its values at
x = 1, 2 ….

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